Question 176960


{{{(a-2b)(a+2b)}}} Start with the given expression.



Now let's FOIL the expression.



Remember, when you FOIL an expression, you follow this procedure:



{{{(highlight(a)-2b)(highlight(a)+2b)}}} Multiply the <font color="red">F</font>irst terms:{{{(a)*(a)=a^2}}}.



{{{(highlight(a)-2b)(a+highlight(2b))}}} Multiply the <font color="red">O</font>uter terms:{{{(a)*(2*b)=2*a*b}}}.



{{{(a+highlight(-2b))(highlight(a)+2b)}}} Multiply the <font color="red">I</font>nner terms:{{{(-2*b)*(a)=-2*a*b}}}.



{{{(a+highlight(-2b))(a+highlight(2b))}}} Multiply the <font color="red">L</font>ast terms:{{{(-2*b)*(2*b)=-4*b^2}}}.



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{{{a^2+2*a*b-2*a*b-4*b^2}}} Now collect every term to make a single expression.



{{{a^2-4*b^2}}} Now combine like terms.



So {{{(a-2b)(a+2b)}}} FOILs to {{{a^2-4*b^2}}}.



In other words, {{{(a-2b)(a+2b)=a^2-4*b^2}}}.



Note: this problem is an example of the use of difference of squares.